What doctrine stated that each state had retained its sovereignty and could reject national acts upon joining the US?

Answer 1

The doctrine of nullification. This doctrine recently been expressed in a different form as the principle of "state sovereignty", which uses the 9th and 10th Amendments to justify laws prohibiting Federal activities. The counter-argument is that the commerce clause of the Constitution allows Congress to regulate interstate commerce, and under that basis can institute programs nominally under state jurisdiction (e.g. national health care).